Axion inflation does not generate any \(B\!-\!L\)  asymmetry.\(10\endcsname \)This immediately follows from the fact that axion inflation does not involve any \(B\!-\!L\) -violating interactions.
In addition, one may explicitly convince oneself that \(B-L = 0\)  at the end of axion inflation by appropriately combining the charge densities in Eq. (REF ).

Therefore, if the radiation-dominated era after inflation is solely described by SM physics, the global \(B\!-\!L\)  charge always remains zero and leptogenesis plays no role in the generation of the BAU.
This situation changes as soon as RHNs are added to the picture.
As pointed out in Ref. [1]}, efficient RHN interactions alter the chemical transport in the plasma such that primordial charge asymmetries can be reprocessed into a new \(B\!-\!L\) -violating equilibrium, even if \(B\!-\!L = 0\)  initially.
This mechanism was dubbed wash-in leptogenesis in Ref. [1]}.
In addition, RHNs can of course lead to the generation of a \(B\!-\!L\)  asymmetry by means of standard thermal leptogenesis.
However, as shown in Ref. [1]}, the thermal contribution to the final BAU is independent of the wash-in contribution, up to numerically negligible corrections.
It therefore suffices to simply add it to the outcome of wash-in leptogenesis.
